Irony is when a statement is not what you expect or seems contradictory.  My favorite ironic statement is this one by Rainsford.

"Don't talk rot, Whitney," said Rainsford. "You're a big-game hunter, not a philosopher. Who cares how a jaguar feels?"

This is very ironic since Rainsford later becomes hunted.  As a hunter, he had no sympathy for his prey.  The hunter is about to become the hunted.

The second best ironic statement is made by General Zaroff.

“We try to be civilized here."

This quote is ironic because Zaroff thinks he is civilized, which we usually think of as the mark of social order.  Social order means following laws and treating people well, and Zaroff hunts and kills people.  When Rainsford objects to Zaroff’s use of the word civilized, he is annoyed and says that men are no more important than other animals.